1 Motivation
Social choice is the theory about collective decision towards social welfare starting from individual opinions, preferences, interests or welfare. The field of Computational Social Welfare is somewhat recent and it is gaining impact in the Artificial Intelligence community. Classical literature makes the assumption of singlepeaked preferences, i.e. there exist a linear order in the preferences and there is a global maximum in this order. Recently some theoretical results were published about Twostage Approval Voting Systems (TAVs), Multiwinner Selection Rules (MWSR) and Incomplete (IPs) and Circular Preferences (CPs) that I claim leads to research about Preferences Graphs and Preferences Multidimensional Functions in Polynomial time.
The purpose of this paper is threefold: Firstly, I want to introduce Social Choice Optimisation as a generalisation of TAVs where there is a maximization stage and a mininimization stage implementing thus a Minimax, a wellknown Artificial Intelligence decisionmaking rule to minimize hindering towards a (Social) Goal. Secondly, I want to introduce, following my Open Standardization and Open Integration Theory (in refinement process) put in practice in my dissertation [1], the Open Standardization of Social Inclusion, as a global social goal of Social Choice Optimization.
As for the Open Standardization of Social Inclusion, I will start finding an open consensus between Adaptive Coordinate descent and Coherence Theory, extending the propositional evaluation of the latter for the multivariate functional case, adjusting thus both domains. Then I will continue towards an open integration of both approaches introducing the Coherent Social Inclusion Problem. Finally, I will provide an algorithm for the Onestage Approval Voting (OAV) and two for the Twostage Approval Voting (TAV), namely, Preference Number Maximization (PNM) and Preference Management (PM). PNM is useful for tackling the overall known problem, but is NPhard in the uncertain case as it is a generalisation of the Travelling Salesman Problem for continuous Halmiltonian Paths. Let me argue this statement. Adaptive Coordinate Descent is a generalisation of Gradient Descent which in turn it is a generalisation of Hill Climbing.
That is my point, imagine that you and some other strangers got kidnapped and left unconscious in the middle of a mountain. Let also assume, that you want to reach a peak to see where are you in order to continue with the escape plan. (Rolling downwards is obviously disregarded). In that case, you might want to follow the most gradual and feasible path minimising the distance walked too. Having a bit of knowledge of the mentioned mountain or having a map would equal to finding the gradual shortest path. However, without any knowledge of the mountain, only with an intuition about the goal, you and your luckily friendly partners should arrive to a consensus about the paths to follow at any bifurcation. One heuristic would be to analyse a subset of all the possible paths, choose the kgradual and feasible paths and vote the final solution. That would be Coherent Social Inclusion.
The structure of this paper is as follow: Section 2.1 introduces the field and latest research results on Social Choice. A generalization of Coherence Theory is introduced in section 2.2. The first approach presented in this paper is Twostage Approval Voting Optimization and it is enunciated in section 3.1. Secondly, the minimization of Discriminating Preferences is introduced in section 3.2. Thirdly, the Coherent Social Inclusion Problem is defined in section 4. The overall process for one and two stages without uncertainty, namely, is presented in section 5. Finally, in section 6 is adapted for a Policymaking scenario.
2 Context
2.1 Social Choice
Social choice is the theory about collective decision towards social welfare starting from individual opinions, preferences, interests or welfare. The field of Computational Social Welfare is somewhat recent and it is gaining impact in the Artificial Intelligence Community. Classical literature makes the assumption of singlepeaked preferences, i.e. there exist a linear order in the preferences and there is a global maximum in this order. Recently some theoretical and polynomial time results were published about Twostage Approval Voting Systems (TAVs), Multiwinner Selection Rules (MWSR) [2] and Incomplete (IPs) [3] and Circular Preferences (CPs) [4] that I claim leads to research about Preferences Graphs and Preferences Multidimensional Functions in Polynomial time.
2.1.1 Twostage Approval Voting
Approval Voting (AV) is a singlewinner electoral system where each voter may select candidates. The winner is the mostapproved candidate. There are extensions for the selection of winners using Multiwinner Selection Rules (MWSR) in Proportional Approval Voting:
Definition 1
‘Let us now give and analyse our IP formulation for PAV. This formulation has one binary variable
for each candidate , indicating whether candidate is part of the committee. Constraint (2) requires that the committee contains exactly candidates. The binary variables indicate whether voter approves of at least candidates in the committee; this interpretation is implemented by the constraints (3)’(1)  
(2)  
(3)  
(4)  
(5) 
Extracted from [2].
Twostage Approval Voting (TAV) is a refinement of AV, where the global Selection Rule is divided into two selection rules that narrows the group of candidates passing to the next stage.
2.2 Coherence Theory
Thagard proposed a decisionmaking Theory of Coherence about a graph of atomic propositional preferences with a computational coherence function that it is modified when newer preferences are added [5].
3 Preliminary Proposals
The author proposes to specify Coherence Theory with a multidimensional Coherence function is each edge of the Graph.
3.1 Optimizing Twostage Approval Voting
Following the classical approach to TAVs, the MWSR selects the kwinners with the most votes in both stages. On the contrary, the Author proposes first a maximisation (most positive votes) stage and then a minimisation (less negative votes) stage. Thus, applying the Minimax Condorcet Method for the optimisation of Social Choice.
3.2 Discriminating Preferences Minimization
Taking from granted Social Inclusion as the global goal of Social Choice Optimization, the author defines Social Discrimination as the inverse of a multidimensional Utility function representing the Social Inclusion of an agent in a Society.
As for minimization, Adaptive Coordinate Descent[6] is a Gradient Descent generalisation for optimization of nonderivable functions, as the Social Discrimination functions.
3.2.1 Declarative Electronic Institutions may Discriminate
Any type of constraint in the Social Universe (either physical, social, normative, moral, ethic, etc.) are implicitly generalized as the Social Discrimination function.
For example, the author envisages several Social Discrimination axis, namely, the agreed (physical, social, normative, moral, ethic) categories leading exclusion and discrimination risk, e.g age (range), gender, ethnicity,…,negative permissions, prohibitions, obligations, duties, power and so on.
In the following applied example I will use Declarative Mechanism Design [7]:
A Declarative Electronic Institution calculates the aggregation and removal of agreed events () for a set of previous (possibly empty), a set of Rules and a set of Events.
Assuming a declaration order and using Social Discrimination definition it would be defined as follows:
A Declarative Electronic Institution assigns a Boolean on the acceptance on the aggregation of some Events at time depending on the previous ones.
Generalizing,the Institutional axis might be:
Nevertheless, events occur concurrently and are processed in tandem, so:
A Declarative Electronic Institutions determines the acceptance of concurrent Events.
Thus, s Social Discrimination function that all the Declarative Electronic institutions might implement would be:
That is, it studies the discrimination degree of agent events over time with regard of a Society.
Definition 2
A Social Discrimination function determines the degree of non acceptance of a set of preferences of a subset of agents with respect of a Society over time:
where are the (possibly infinite) dimensions in , the Discrimination Space and:
where calculates the agreed discrimination degree of a set of Preferences and;
where calculates the agreed discrimination degree of a set of Traits .
Definition 3
A Knowledge Map is a (partial and globally agreed) implementation of in dimensions of the Social Discrimination space such that:
where is the degree of Uncertainty and is the degree of Social Discrimination.
For instance, Gravity Law on Earth has and since it is worldwide agreed that limits all (Human) Societies equally. Similarly, Absolute Majority rule has although since it is the worldwide accepted Decision Rule even if it discriminates other preferences and candidates in the decision process.
Let me then introduce the Social Inclusion Problem and a characterization of its possible solutions.
4 Coherent Social Inclusion
4.1 Coherent Social Inclusion Problem
Definition 4
For a Social Universe where there exist , the set of all agents in , a set of Society functions such that , and a set of Social Inclusion Problems in dimensions, such that the ith problem:
where:
A Social Power order between Socities due to the Social Utility calculated as the sum of weighted average Utilities (of presumed traits) of all the agents in the Society, is the set of all presumed traits of the set of agents . is the set of Social Discrimination Profile functions in dimensions over for all the agents in . is the set of all preferences in . is the Selected Preferences function such that ; namely the subset of preferences taken into account for preference aggregation. Finally, is the Social Discrimination function over in dimensions,as per definition 3.
The Social Discrimination Profile functions
are discrimination estimations agreed upon previously over the Social Roles of a Society. Namely, they are a set of vectors
in the Social Discrimination Space.Definition 5
As for agency, an agent :
where is the trait of agent ; is the set of all the traits of agent , where is the Utility trait for agent , is the Social Discrimination Profile function of agent in dimensions, such that . Moreover, is the (Possible and Coherent) Preference Knowledge of agent such that where each is a Preference Discrimination function of agent in dimensions such that ; is the preference of agent . Subsequently, is the Preference function of agent such that .
4.2 Coherent Social Inclusion Solutions
Definition 6
is a solution for a Social Universe that finds a Coherent Inclusion Problem that maximises Social Power and minimizes Social Discrimination .
Definition 7
Coherent PolicyMaking is a function:
where is a solution of Coherent Social Inclusion at time .
Definition 8
Optimal PolicyMaking is a function:
where is the best solution of Coherent Social Inclusion at time .
4.3 Discrimination
The notion of social discrimination has been defined thoroughly from a qualitative perspective. In this paper, the author wants to create a quantitative definition of social discrimination as follows:
Definition 9
Social Discrimination are the limitations of a (sub)society imposed by another society. It may also use Graded Ostracism, namely, forcing demote to a subsociety in the Social Power order.
In definition 4 Social Power orders subsocieties for their Social Utility introduced as the sum of the weighted average of (pressumed traits ) for all agents in the subsociety. This weighted average may vary from subsociety and generalises Social Prejudices, like racial, sexual orientation and so on.
Definition 10
When the number of subsocieties tends to infinity, Social Power function is defined as:
for a society is the supersociety of Social Universe .
Definition 11
When the number of subsocieties tends to infinity, Social Utility is defined as:
where is the maximal society of Social Universe , a supersociety.
Definition 12
When the number of subsocieties tends to infinity, :
for the maximal society of Social Universe , the supersociety.
Definition 13
When , Social Power function is defined as:
where is a the minimal society of Social Universe formed only by a agent.
Definition 14
When , Social Utility is defined as:
where is a the minimal society of Social Universe formed only by a agent.
Definition 15
When :
where is a the minimal society of Social Universe formed only by a agent.
4.4 Capitalism
Definition 16
When , Utility for all agent in Social Universe tends to infinity, :
and
where is a minimal society of Social Universe formed only by a agent.
Definition 17
When , Utility for all agent in Social Universe tends to infinity, :
and
where a the maximal society of Social Universe , a supersociety.
Definition 18
When , Utility for all agent in Social Universe tends to infinity, :
and
where a the maximal society of Social Universe , a supersociety.
Definition 19
When :
Definition 20
When :
That shows some Properties of Capitalism, under Social Power and Social Discrimination, and leads to try to find a compromise of Social Discrimination versus Societal Autonomy in a Policymaking scenario.
This may be be achieved by decreasing the weight of Utility on the contribution to Social Utility, may be remunerating each vote that contributes to the Society, as Participatory Utility
. Concretely, by using Linear Programming with these constraints and the following methods:
5 CSI Algorithms without Uncertainty
5.1 Onestage Approval Voting
is the Onestage Coherent Social Inclusion function for a Society such that maximizes by voting the set of agents such that there exist a Inclusive Multiwinner Selection Rule function:
where is the Coherent Social Inclusion Society such that maximises by voting the number of agents belonging to such that :
.
That is, we would like to maximize the number of agents with the minimum traits being discriminated for. For the calculation of this Onestage Coherent Social inclusion function, we firstly apply the Adaptive Coordinate Descent algorithm to find a set of less socially discriminatory all the preferences P, and then we apply the onestage of the Approval Voting system where we maximize the number of winners with no trait being discriminated for.
5.2 Twostage Approval Voting
5.2.1 Preference Number Maximization
is the Two stage Coherent Social Inclusion function for a Society such that maximizes by voting the set of agents such that there exist a Twostage Inclusive Multiwinner Selection Rule function:
where is the Coherent Social Inclusion Society such that maximises by voting the number of agents belonging to such that :
 Stage one

 Stage two

1.
3.
That is, we would like to maximize the number of agents with the minimum traits being discriminated for. For the calculation of this Coherent Social inclusion function, we firstly use a Multiple Winner Selection Rule, , on all preferences , as per definition 1. Then we apply the Adaptive Coordinate Descent algorithm on the composition of the Social Discrimination function and Social Discrimination profile of the result of previous stage. Finally, , namely the MultiWinner Selection Rules of the second stage is used to find a set of less socially discriminatory winning preferences.
If the number of agents were very large, this algorithm would perform poorly. That is the main reason for the next and final algorithm, suitable for Policymaking.
6 Social Choice Optimization in Policymaking
In this Policymaking scenario, the author acknowledge some degree of Uncertainty in the Social Discrimination function without entering in the Agency Uncertainty scenario where the traits of the agents are unknown.
In this section, although two possibilities are considered, namely, Preference Aggregation (Addition) and Preference Derogation (Removal), later on we will see that both cases are forwardchaining, renaming thus the algorithm to Preference Management.
6.1 Preference Aggregation
Assuming that a Society already exists and starts with a Coherent Inclusion Problem and minimum set of norms including a Coherent Social Inclusion function, one could assume that if the norms are already Socially Coherent, namely, they minimize the discrimination of the Society. Then the objective is to apply the Coherent Social Inclusion function to add new preferred norms that continues coherently including the whole society.
is the Twostage Preference Aggregation Coherent Social Inclusion function for a Society such that maximizes by voting the set of agents such that there exist a Lessdiscriminatory Multiwinner Selection Rule function:
where is the Coherent Social Inclusion Society such that maximises the number of agents belonging to such that :
 Stage one

 Stage two

1.
2.
3.
That is, we would like to maximize by voting the number of agents with the minimum traits being discriminated for. For the calculation of this Coherent Social inclusion function, we firstly use a Multiple Winner Selection Rule, , on a subset of all preferences , to start with the aggregation process. As it should return a coherent subset of preferences, even a random subset might be used to start the initialization process. Then we apply the Adaptive Coordinate Descent algorithm on the Social Discrimination function of the result of previous stage; and then the secondstage to find a set (of size ) of less socially discriminatory winning preferences.
For this, once found the less discriminatory goal(s) as the singlepeak preference(s) we then may find the shortest path(s) in , a graph with a multidimensional discrimination function in each edge. In order to do this, each cost in the graph can be calculated by the application of the discrimination function from vertex to vertex. With the shortest path(s), i.e. the optimum (set of) singlepeaked preferences, we may now apply the second voting stage (possibly categorised by each path of the set) to find the kCoherent Optimum Preferences to aggregate.
6.2 Preference Derogation
When dealing with Uncertainty and Local Minima, it might be necessary to remove some previously agreed preferences and continue with the Aggregation process. It would be extremely useful in a Policymaking scenario.
In practice, the cost of adding or removing a Preference are different, and may involve more than one Preference depending on the direction. In this case, as a matter of fact, paths in the Social Discrimination function cannot be transited backwards, as generally, there are some actions that does not have inverse, or they are irreversible.
Then, as for the metaphor, the map of the mountain is moreover a directed Graph, like in Vehicle onedirection maps. Thus, we need to redefine our Preference graph to be directed and with possibly different Social Discrimination functions associated with each direction between two vertices.
Thus, the PA algorithm could be renamed as Preference Management algorithm in this case, since we can only advance through the graph towards the Global Social Inclusion goal, possibly not optimally if derogation is necessary and mainly due to nonoptimal collective decisions in Stage 2 of .
6.3 Compacting the Social Discrimination function
After a long process of Preference Aggregation and Derogation, the history of the travelled path may contain circles, namely returning to a previous edge in the graph. Thus, for compacting the Preference History one may remove cycles when reaching a previous transited point to obtain a Preference Set. However, it is not desirable to decrease Certainty in a a priori Uncertain function as Social Discrimination in order to optimally and automatically learn from errors with the method proposed.
6.4 Preferences over Social Discrimination functions
The Coherent Social Inclusion Problem is recursive by nature: agents need to Coherently Agree in a Social Discrimination function first. So the General Problem is: Could we arrive to agreements on our Preferences over the Agreed Social Discrimination function? A feasible solution to kickstart the method is to apply the method over Preferences over Social Discrimination functions based on current Social Discrimination functions: the definition of our States, Constitutions, and so on.
In a Society initialization case, it may start empty and the selected preferences to vote be chosen randomly, bootstrapping thus in a Brainstorming fashion.
6.5 Uncertainty in the Social Discrimination Space
In the Coherent Social Inclusion Problem presented at the beginning of section 4 there were additional definitions such as . It was left on purpose to make noticeable the case where the Social Discrimination Function, the map of the mountain (the Social Discrimination Space), is not completely known in advance. Thus, it would require to coherently and iteratively aggregating Preference Discrimination Functions of agents, namely, some for all agent .
One tentative solution involving Regulated Deep Learning would be using
in a Regulated Learning phase (Maxphase) where some agreements are made when learning, and employ concurrently in a Regulated Decision phase (Minphase), as the one presented in section 6.1 for establishing the Inclusive and Coherent Preference Agreements under Partial Uncertainty.7 Justification Example
To further exemplify, the proposal of this paper, let assume the problem of creating traffic signals in a whole country. We will start assuming two subsocieties in the country, the pedestrianonly and the cardrivers ones:
For brevity, we will also assume that there are four proposals to be voted: ,, and where, respectively correspond to the cases with no signal, create only crosswalks, create only traffic lights and mixed presolved approaches are:
After recursive application of the proposed method, we will also assume we arrive to the following considerations:

for :

for :

for :

for :
For a toy example like this, it may seem obvious that the better approach is in terms of equality of Social Power and Social Discrimination. However there might be societies where (cities) or (small villages) such that the Absolute Majority Rule would not work optimally regarding Social Inclusion, since in those cases and would win a priori win due to the population unbalance. Especially for those cases, the Lessdiscriminatory Majority Winner Selection Rule will optimize policymaking.
8 Conclusions
In this paper is I have introduced Social Choice Optimisation as a generalisation of Twostage Approval Voting (TAV) where there is a maximization stage and a minimization stage implementing thus a Minimax, a wellknown Artificial Intelligence decisionmaking rule to minimize hindering towards a (Social) Goal. Secondly, I have presented, following my Open Standardization and Open Integration Methodology (in refinement process) I put in practice in my dissertation [1], the Open Standardization of Social Inclusion, as a global social goal of Social Choice Optimization. Any type of constraint in the Social Universe (either physical, normative, moral, ethic, etc) are implicitly generalized in the Social Discrimination function.
As for the Open Standardization of Social Inclusion, I started with a open consensus between Adaptive Coordinate descent and propositional Coherence Theory, extending the latter for the functional case. Then I continued towards an open integration of both approaches introducing the Coherent Social Inclusion Problem. Finally, I provided an algorithm for the Onestage Approval Voting (OAV) and two for the Twostage Approval Voting (TAV), namely, Preference Number Maximization (PNM) and Preference Aggregation (PA). PNM is useful for tackling the overall known problem, but is NPhard in the uncertain case as it is a generalisation of the Travelling Salesman Problem for continuous Halmiltonian Paths. Let me argue this statement. Adaptive Coordinate Descent is a generalisation of Gradient Descent which in turn it is a generalisation of Hill Climbing. That is my point, imagine that you and some other strangers got kidnapped and left unconscious in the middle of a mountain. Let also assume, that you want to reach a peak to see where are you in order to continue with the escape plan. (Rolling downwards is obviously disregarded). In that case, you might want to follow the most gradual and feasible path minimising the distance walked too. Having a full of knowledge of the mentioned mountain or having a map would equal to finding the gradual shortest path. (NP=P). However, without any knowledge of the mountain, only with an intuition about the goal, you and your luckily friendly partners should arrive to a consensus in which paths to follow at any bifurcation. One heuristic would be to analyse a subset of all the possible paths, choose the kgradual and feasible paths and vote the final solution. That would be Coherent Social Inclusion: the Lessdiscriminating Majority Winner Selection Rule (LDMWSR).
9 Future Work
The main goal of this paper is that , namely the Lessdiscriminating Majority Winner Selection Rule () would be included in each Constitution, i.e. each core of constitutive rules establishing the basis of every (Human) Society.
For the time being, Social Choice Optimization opens new opportunities for multidisciplinary research: from theoretical to applications in almost every field of Knowledge, going through all the possibilities in between as I would briefly introduce;starting though with the mention of recent work [8][9] that might seem hopeful for characterising the as Pareto.
9.1 Policymaking Opmitization
One could integrate the problem, constraints on Social Power and methods presented in a Linear Programming problem to maximize Social Power and minimize Social Discrimination. The author expects to follow in shortterm this research path using Neurodynamic programming [10] from a Simulationbased Optimization perspective where a vehicle routing problem[11] is extended with lowsocial power pedestrians and, (crosswalk or traffic light) norm allocations to solve this Coherent Social Inclusion problem, from a (toy) singlecross problem to a (real) worldwide problem. Although promising results are presented in [12] and [13], the advantages of the proposal of this paper are that (norm) preferences are explicit and known for the problem to be solved contrary to the blackbox approach of Neurodynamic programming for each function to be learned. However, a preference history (policy) could be found for each voting step with the mentioned approach.
9.2 Abstraction and Aggregation in
Defining a computer program, norm, constraint solving and so on is finding and constructing a function in the Lebesgue space . By defining the Social Discrimination function as a functional abstraction in Lebesgue space opens the research path of Computational Abstraction (definition, formalisation, characterization, implementation), maybe be as functions in hyperconnected Domains, involving all the Artificial Intelligence fields: Logics, Reasoning, Learning, Multiagent Systems, Declarative Mechanism Design, and so on.
As a starting point, functions in different Domains (topics) define a new superdomain. Thus, I refer to superdomains created by two functions created with Lambda calculus. Then, recursively, using Lambda Calculus of two (or more) of these superdomains, and so on. I would name these two Lambda calculus of superdomains: Standardization and Integration.
9.3 Characterization of Social Choice Optimization
Starting in a topdown approach, I would mention than the most prominent theoretical research path would be the formalization of Social Choice Optimization properties. From checking what paradoxes apply and how much Condorcet Efficient would be. I followed a Hill climbing (citation following) approach starting from [14] to [3] and the path has been at least interesting.
9.4 Improving Coherent Social Inclusion
9.4.1 Learning Social Discrimination Profile
The Social Discrimination Profile functions are discrimination estimations agreed upon previously over the Social Role of a Society. I have assumed than Discrimination may be analysed quantitatively. However, this is still an ongoing research path as [15] and [16] present. This poses the next research question: Could Regulated Deep Learning [7] learn a discrimination function from empirical tests?
9.4.2 Relaxing the number of traits and social profiles being discriminated
In the Onestage Approval Voting algorithm for Coherent Social Inclusion, all the preferences of the Social Universe are taken into account. One research path would be characterizing and proposing solutions for the relaxed case where the number of traits, or social profiles, being discriminated is not an empty set.
9.5 Increasing Uncertainty: Collaborative Knowledge Exploration
Continuing with the Mountain Exploration metaphor, where I assumed all the kidnapped members of the Society are together in the same point of the Mountain and must remain together. Let me then assume a variation where the agents are scattered all over the Mountain, namely Discrimination Space. Then, one could start assuming that there exist Free Communication and the global (and common) social goal of everyone reaching at the highest peak, is maintained. In this case, the application domain is multidisciplinary.
9.5.1 Assuming Agent Rationality and Will
Following the extra definitions, we may find the (Possible and Coherent) Knowledge function over a set of preferences and a set of Preference Discrimination functions for agent . We may define and implement the Agent Preferences function
strategically following a Game Theory approach, dividing the Strategic Preference (and Preference Discrimination) Selection problem in possibly continuous steps, like continuous time.
9.6 Implementing Coherent Social Inclusion in Declarative Mechanism Design.
Following the work from [7] on Declarative Mechanism Design, where is improved, the author expects to start the Open Integration of Coherent Social Inclusion in the forementioned Regulated Middleware.
Furthermore, the work presented previously in [1] has been tested in the Electronic Institutions (EIs) Middleware presented in [17] that runs over JADE [18]. Nonetheless, the author expects to add the language to a newly developed Middleware, as it is capable of give Operational Semantics, i.e run, a Declarative version of EI protocols as it was shown in [1]. The main advantage of a Declarative version is that it might be provided to Software Agents as the rulesofthegame in order to coordinate, e.g, using Social DCOPs [19], AMODCOPs [20] or Game Theory.
9.7 Improving Game Theory
From the complete implementation of Declarative Electronic Institutions found in [1] we have just used one Activity, a Metamorphic Game, i.e. a game whose rules may vary with time, action (or inaction) of agents, or other normative notions. To the best of my knowledge there are several types of Games not formalised yet in order to fully coordinate agents in a Declarative (Complete) Electronic Institution. Thus, there might be a need to formalise Hierarchical Concurrent Metamorphic Game Theory. However, following the DivideandConquer methodology a first attempt of roadmap would be in the inverse order:
Then, it would reasonable to study their interrelationships, thus creating Declarative MetaGames, as the computable with the Declarative Electronic Institutions tested.
9.8 FullHybrid Artificial Intelligence
However, using
as an Programmable Eventbased Middleware opens new paths of research as it uses Hybrid AI (ı.e. mixes Autonomous Agents and Multiagents Systems, Machine Learning, and Symbolic Programming). Furthermore, one of the main applications of Hybrid AI is in its own a whole new AI subfield, namely, Artificial Teaching.
9.9 Artificial Teaching
The whole concept of Artificial Teaching is recent, and not properly defined yet. There are some mentions in the literature that I will not cite in order to engage the reader to improve the previous lines and the proposed concepts luckily exposing her results on subsequent articles. For a sample, the reader may check ongoing research in [21] and [22].
In my humble opinion, in the research path towards General AI there are several Problemspecific milestones to reach in every subfield of AI; and mimicking Human Intelligence and Evolution, it may seem a natural step forward to add the teaching capability to artificial learners to decrease complexity.
Please imagine a researcher (agent) being in a continuous ”Deep… and deep… and deep… and very deep… Learning” process since the beginning of its existence. To the best of my knowledge, there are very few (human) researchers (honestly, almost none) that selflearned everything on his own, with no interaction with others who may have taught him something, even involuntarily, and this happens almost every day as a Spanish proverb well says.
9.10 Collaborative Knowledge Evolution
Sumarizing my main goal as Collaborative Knowledge Evolution, it could be seen as the Open Standardization and Integration of Open Knowledge optimized from generation to generation thanks to (Human) Evolution. With this, I want to emphasize the role of (Human and Artificial; Physical and Software) Teachers in Collaborative Learning and (Collaborative) Research, and thus in Collaborative Knowledge Evolution. Luckily, in a future we would be a step closer to General AI, by means of Collaborative Optimisation, achieving thus a full integration and consensus of researchers (and their contributions, either Physical or Software), even they are not collaborating on purpose. And all these thanks to Regulated Middlewares and Artificial Mediators.
References
 [1] A. GarcíaCamino, Normative regulation of open multiagent systems, Monografías del IIIA Vol. 35, Consejo Superior de Investigaciones Científicas, 2010.
 [2] D. Peters, SinglePeakedness and Total Unimodularity: New PolynomialTime Algorithms for MultiWinner Elections, in: The ThirtySecond AAAI Conference on Artificial Intelligence (AAAI18), Association for the Advancement of Artificial Intelligence (AAAI), 2018, pp. 1169–1176–.
 [3] Z. Fitzsimmons and M. Lackner, Incomplete Preferences in Single Peaked Preferences., Journal of Artificial Intelligence Research (2020), 797–833.
 [4] D. Peters and M. Lackner, SinglePeaked Preferences on a Circle, in: The ThirtyOne AAAI Conference on Artificial Intelligence (AAAI17), Association for the Advancement of Artificial Intelligence (AAAI), 2016.
 [5] P. Thagard, Coherence in Thought and Action, MIT Press, 2002.

[6]
I. Loshchilov,
M. Schoenauer and
M. Sebag,
Adaptive Coordinate Descent,
in:
Genetic and Evolutionary Computation Conference (GECCO).
, ACM Press., 2011, pp. 885–892–.  [7] A. GarcíaCamino, Declarative Mechanism Design. A testbed for Regulated Deep Learning., AI Communications (2019). http://arxiv.org/abs/1912.13122.
 [8] J.S. Kelly, Characterization of the Pareto social choice correspondence, Mathematical Social Sciences (2020). doi:https://doi.org/10.1016/j.mathsocsci.2020.05.003.
 [9] C. Duddy and A. Piggins, A foundation for Pareto optimality, Journal of Mathematical Economics 88 (2020), 25–30. doi:https://doi.org/10.1016/j.jmateco.2020.02.005.
 [10] D.P. Bertsekas and J.N. Tsitsiklis, Neurodynamic programming: an overview, in: Proceedings of 1995 34th IEEE Conference on Decision and Control, Vol. 1, IEEE, 1995, pp. 560–564.
 [11] N. Secomandi, Comparing neurodynamic programming algorithms for the vehicle routing problem with stochastic demands, Computers & Operations Research 27(11–12) (2000), 1201–1225.
 [12] J. Zhao, M. Gan and C. Zhang, Eventtriggered optimal control for continuoustime nonlinear systems using neurodynamic programming, Neurocomputing 360 (2019), 14–24.
 [13] X. Yang and H. He, EventDriven Constrained Control Using Adaptive Critic Learning, IEEE Transactions on Cybernetics (2020).
 [14] W.V. Gehrlein and D. Lepelley, Voting Paradoxes and Group Coherence. The Condorcet Efficiency of Voting Rules, Studies in Choice and Welfare, Springer, 2011.
 [15] M. Schaerer, C. du Plessis, A.J. YAP and S. THAU, Low power individuals in social power research: A quantitative review, theoretical framework, and empirical test., Organizational Behavior and Human Decision Processes. (2020), 73–96. doi:https://doi.org/10.1016/j.obhdp.2018.08.004.
 [16] G.R. Bauer and A.I. Scheim, Methods for analytic intercategorical intersectionality in quantitative research: Discrimination as a mediator of health inequalities., Social Science & Medicine. (2019), 236–245.
 [17] M. Esteva, Electronic Institutions: from specification to development, PhD thesis, Universitat Politecnica de Catalunya, 2003, Number 19 in IIIA Monograph Series.
 [18] F. Bellifemine, A. Poggi and G. Rimassa, JADE  A FIPAcompliant agent framework, Technical Report, Telecom Italia., 1999, Part of this report has been also published in Proceedings of PAAM’99, London, April 1999, pp.97108..
 [19] A. Netzer and A. Meisels, SOCIAL DCOP  Social Choice in Distributed Constraints Optimization, in: Intelligent Distributed Computing V, F.M.T. Brazier, K. Nieuwenhuis, G. Pavlin, M. Warnier and C. Badica, eds, Springer Berlin Heidelberg, Berlin, Heidelberg, 2012, pp. 35–47. ISBN ISBN 9783642240133.
 [20] T. Matsui, M. Silaghi, T. Okimoto, K. Hirayama, M. Yokoo and H. Matsuo, Leximin asymmetric multiple objective DCOP on factor graph, in: International Conference on Principles and Practice of MultiAgent Systems, Springer, 2015, pp. 134–151.
 [21] D.K. Kim, M. Liu, S. Omidshafiei, S. LopezCot, M. Riemer, G. Habibi, G. Tesauro, S. Mourad, M. Campbell and J.P. How, Learning Hierarchical Teaching Policies for Cooperative Agents, in: Proceedings of the Conference in Autonomous Agents and Multiagent Systems (AAMAS’20), International Foundation for Autonomous Agents and Multiagent Systems (IFAAMAS)., 2020, pp. 620–628.

[22]
F.L.D. Silva, G. Warnell, A.H.R. Costa and P. Stone, Agents Teaching Agents: A Survey on Interagent Transfer Learning, in:
Proceedings of the Conference in Autonomous Agents and Multiagent Systems (AAMAS’20), International Foundation for Autonomous Agents and Multiagent Systems (IFAAMAS)., 2020, pp. 2165–2167.
Comments
There are no comments yet.